Communication system

ABSTRACT

A communication system that can satisfactorily communicate with a mobile station by a transmitter and receiver of a simple arrangement, wherein a plurality of carriers having different frequencies are transmitted simultaneously and data is transmitted on the basis of a phase difference between the carriers. Also, the carriers are multiplied with a predetermined time waveform and transmitted, so that a reception side receives data by use of a time waveform narrower than the above time waveform.

This is a division of prior application Ser. No. 08/524,215 filed Sep.6, 1995.

BACKGROUND OF THE INVENTION

The present invention relates to a transmission system for use incommunicating with a mobile station.

A variety of mobile communication systems, such as a mobile telephone orportable telephone for communicating with a mobile station haveheretofore been put into practice. The mobile communication system isfundamentally the same communication system is that for communicatingwith fixed stations.

A reception signal received at a mobile communication terminal, such asmobile telephone or portable telephone tends to be distorted due to theinfluence of multipath fading. Specifically, when the multipath fadingoccurs, a propagation delay between paths increases to cause anintersymbol interference. As a consequence, preceding and succeedingcodes overlap each other to deteriorate a transmission characteristic.

In order to satisfactorily receive a reception signal even when thetransmission characteristic is degraded, a sync (synchronizing)detecting circuit formed of an adaptive equalizer or a PLL (phase-lockedloop) circuit has to be applied so that a receiver becomes complex inarrangement and expensive.

Furthermore, when a modulated waveform to be transmitted is changed witha probability distribution which is often referred to as a Gaussiandistribution, a peak-to-peak value takes a large amplitude so that asignal transmitted via a transmission amplifier or the like is distortedand a spectrum of a modulated wave is widened to exert an adverseinfluence on the adjacent channel.

SUMMARY OF THE INVENTION

In view of the aforesaid aspect, it is an object of the presentinvention to provide a communication system which can satisfactorilycommunicate with mobile stations by a transmitter and receiver of asimple arrangement.

According to a first aspect of the present invention, there is provideda communication system which is comprised of transmission processingmeans for transmitting a plurality of carriers having differentfrequencies simultaneously and transmitting data on the basis of a phasedifference between the carriers.

According to a second aspect of the present invention, there is provideda communication system which is comprised of modulating means foroutputting a modulated output waveform in which an amplitude probabilitydistribution is approximate to a Gaussian distribution, a limiter foramplitude-limiting an output waveform of the modulating means, and afilter for filtering out an output of the limiter, wherein the limiteramplitude-limits the mixed signal at a rate of about 1.5 times ofstandard deviation of amplitude distribution or greater and an output ofthe filter is transmitted.

According to a third aspect of the present invention, there is provideda communication system which is comprised of means for transmitting aplurality of carriers having different frequencies simultaneously,wherein a predetermined time waveform is multiplied with each ofcarriers.

According to a fourth aspect of the present invention, there is provideda communication system wherein signals are phase-modulated by aplurality of carriers having different frequencies and transmittedsimultaneously. The communication system is comprised of carriergenerating means for generating carriers and transmitting means forsupplying phase values to the carrier generating means as initial phasevalues and sequentially adding phase values to the carriers at everysample interval to directly obtain data modulated into carriers.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing an arrangement of a transmissionprocessing system of a communication system according to a firstembodiment of the present invention;

FIGS. 2A to 2E are diagrams used to explain examples of carriersaccording to the first embodiment of the present invention;

FIG. 3 is a block diagram showing an arrangement of a transmissionsignal output portion according to the first embodiment of the presentinvention;

FIGS. 4A to 4C are schematic diagrams used to explain the changes ofamplitude distributions of waveforms in the transmission signal outputportion according to the first embodiment of the present invention;

FIGS. 5A to 5C are waveform diagrams showing the changes of waveforms inthe transmission signal output portion according to the first embodimentof the present invention;

FIG. 6 is a block diagram showing an arrangement of a reception signalprocessing system of the communication system according to the firstembodiment of the present invention;

FIG. 7 is an explanatory diagram showing an integrating period of areception processing according to the first embodiment of the presentinvention;

FIG. 8 is a block diagram showing a transmission processing system ofthe communication system according to a second embodiment of the presentinvention;

FIG. 9 is an explanatory diagram showing a time waveform for modulationaccording to the second embodiment of the present invention;

FIG. 10 is a block diagram showing an arrangement of a transmissionprocessing system of a communication system according to a thirdembodiment of the present invention;

FIG. 11 is a block diagram showing an arrangement of a transmissionprocessing system of a communication system according to a fourthembodiment of the present invention;

FIG. 12 is a block diagram showing an arrangement of a transmissionprocessing system of a communication system according to a fifthembodiment of the present invention;

FIG. 13 is a block diagrams showing a specific arrangement of a waveformgenerator used in the fifth embodiment of the present invention;

FIG. 14 is a block diagram showing an arrangement of a receptionprocessing system of a communication system according to a sixthembodiment of the present invention;

FIG. 15 is an explanatory diagram showing a time waveform fordemodulation according to the sixth embodiment of the present invention;

FIG. 16 is a block diagram showing an arrangement of a receptionprocessing system of a communication system according to a seventhembodiment of the present invention;

FIG. 17 is a block diagram showing an arrangement of a receptionprocessing system of a communication system according to an eighthembodiment of the present invention;

FIG. 18 is a block diagram showing an arrangement of a receptionprocessing system of a communication system according to a ninthembodiment of the present invention;

FIGS. 19A and 19B are explanatory diagrams showing time waveforms fordemodulation according to the ninth embodiment of the present invention;

FIG. 20 is a waveform diagram showing attenuated states of frequenciesother than a desired frequency by the time waveform;

FIG. 21 is an explanatory diagram showing examples of waveforms whereina calculation of FFT is carried out; and

FIG. 22 is a waveform diagram used to explain a time waveform.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A first embodiment of the present invention will hereinafter bedescribed with reference to FIGS. 1 through 7.

In this embodiment, the present invention is applied to a communicationsystem wherein digital data is transmitted via radio waves. Digital datais transmitted by a transmission processing system shown in FIG. 1.

As shown in FIG. 1, 8-bit data is sequentially supplied to atransmission data input terminal 1 and 8-bit data is processed as onemodulation unit by the circuit according to this embodiment. The 8-bitdata is divided into 2-bit data each. The 2-bit data thus divided aresupplied to transmission data/phase data converters 2, 3, 4, 5. Thetransmission data/phase data converters 2 through 5 generate phase databased on the states of 2-bit data [X, Y] supplied thereto. As the statesof the 2-bit data [X, Y], there are considered four states expressed onthe following table 1. The transmission data/phase data converters 2through 5 generate different phase data Δφ at every four states.

TABLE 1 X Y Δφ 0 0 π/4 1 0 3/4 π 1 1 −3/4 π 0 1 −π/4

Δφ₀, Δφ₁, Δφ₂ and Δφ₃ represent the phase data that the fourtransmission data/phase data converters 2, 3, 4 and 5 output.

There is provided a reference phase data generator 6 which generatesreference initial phase data φ₀. The initial phase data φ₀ is suppliedto a phase multiplier 7 and a carrier multiplier 11. The phase data Δφ₀output from the transmission data/phase data converter 2 is supplied tothe phase multiplier 7 which multiplies the initial phase data φ₀ andthe phase data Δφ₀ supplied thereto to provide phase data φ₁. Theresultant phase data Δ₁ is supplied to a phase multiplier 8 and acarrier multiplier 12.

The phase data Δφ₁ output from the transmission data/phase dataconverter 3 is supplied to the phase multiplier 8 which multiplies thephase data φ₁ and the phase data Δφ₁ supplied thereto to provide phasedata φ₂. The resultant phase data φ₂ is supplied to a phase multiplier 9and a carrier multiplier 13.

The phase data Δφ₂ output from the transmission data/phase converter 4is supplied to a phase multiplier 9 which multiplies the phase data φ₂and the phase data Δφ₂ supplied thereto to provide phase data φ₃. Theresultant phase data φ₃ is supplied to a phase multiplier 10 and acarrier multiplier 14.

The phase data Δφ₃ output from the transmission/phase data converter 5is supplied to a phase multiplier 10 which multiplies the phase data φ₃and the phase data Δφ₃ supplied thereto to provide phase data φ₄. Theresultant phase data φ₄ is supplied to a carrier multiplier 15.

Therefore, the multipliers 7, 8, 9, 10 multiply the phase data Δφ₀ toΔφ₃ with the initial phase data φ₀, in that order, to provide the phasedata φ₁ to φ₄.

Carrier signals having different frequencies are supplied to first,second, third, fourth and fifth carrier input terminals 16, 17, 18, 19,20, respectively. The frequencies of the carrier signals supplied to theinput terminals 16, 17, 18, 19, 20 are each different by a constantangular frequency ωs. Specifically, the first, second, third, fourth andfifth carrier signals are changed as shown in FIGS. 2A, 2B, 2C, 2D and2E. In actual practice, each carrier signal is a complex number signal.

The carrier multiplier 11 multiplies the carrier signal supplied to thefirst carrier input terminal 16 with the (initial) phase data φ₀. Thecarrier multiplier 12 multiplies the carrier signal supplied to thesecond carrier input terminal 17 with the phase data φ₁. The carriermultiplier 13 multiplies the carrier signal supplied to the thirdcarrier input terminal 18 with the phase data φ₂. The carrier multiplier14 multiplies the carrier signal supplied to the fourth carrier inputterminal 19 with the phase data φ₃. The carrier multiplier 15 multipliesthe carrier signal supplied to the fifth carrier input terminal 20 withthe phase data φ₄. As a consequence, the respective multipliers advancethe phases of the carrier signal by the amounts indicated by the phasedata.

Multiplied outputs from the carrier multipliers 11 to 15 are supplied toand mixed by a mixer 21. A mixed output signal from the mixer 21 issupplied to a transmission signal output terminal 22.

In the modulation effected by multiplication in each of the carriermultipliers 11 to 15, assuming that T is a time during which the angularfrequency ωs, which is a frequency difference between carriers, isadvanced by 2π, then one modulation unit Tm is expressed as:

Tm=(1+α)T  (1)

Specifically, one modulation unit is a time which results from adding αTto the time T during which the angular frequency ωs advances by 2π.FIGS. 2A through 2E are diagrams showing carriers obtained at onemodulation unit. Although a phase difference is indicated only duringthe period T located at the central portion of one modulation unit, thesame modulation is carried out during periods (α/2)T before and afterthe central portion T in actual practice.

Then, as shown in FIG. 3, the signal obtained at a transmission signaloutput terminal 22 is frequency-converted to a signal of a predeterminedtransmission channel (transmission frequency) and supplied to anantenna, which will be described later on, thereby making it possible toeffect radio communication. In this embodiment, a transmission signaloutput unit can be arranged as shown in FIG. 3.

As shown in FIG. 3, the transmission signal obtained at the transmissionsignal output terminal 22 is supplied to a limiter 31 and an amplitudeof the transmission signal is limited by the limiter 31. This limiter 31effects a complex signal processing and an amplitude limiting carriedout by the limiter 31 will be described below. As shown in FIG. 4A,there is the large possibility that an amplitude a of a waveform of thetransmission signal will be changed in the form of Gaussiandistribution. Therefore, as shown in FIG. 4B, the limiter 31 carries outa processing for limiting an amplitude about 1.5 times or higher than astandard deviation.

Then, an output of the limiter 31 is supplied to a filter 32 as shown inFIG. 3. The filter 32 is composed of a low-pass filter (LPF) to cancelout a high frequency band component of the signal limited by the limiter31 so that the distribution of the amplitude a of the transmissionsignal is set in the state shown in FIG. 4C.

Therefore, the waveform of the actual transmission signal changes asshown in FIGS. 5A, 5B and 5C. Specifically, when a modulated waveformshown in FIG. 5A is developed at the terminal 22, the maximum amplitudeportion of this waveform is limited by the limiter 31 and thereby awaveform shown in FIG. 5B is obtained. Further, The filter 32 cancelsout the high frequency band component of the waveform portion thusamplitude-limited to provide a waveform shown in FIG. 5C.

A transmission signal thus processed and output from the filter 32 issupplied to a frequency converter 33. The frequency converter 33frequency-converts the transmission signal supplied thereto by use of atransmission carrier corresponding to a transmission frequency suppliedto a transmission carrier input terminal 34 to provide afrequency-converted transmission signal. The frequency-convertedtransmission signal from the frequency converter 33 is amplified by apower amplifier 35 and supplied to a transmission antenna 36, from whichit is transmitted via radio waves.

An arrangement for receiving the thus transmitted signal will bedescribed with reference to FIG. 6. As shown in FIG. 6, the signal thustransmitted from the antenna 36 (shown in FIG. 3) is received at areception antenna 51. The signal received at the antenna 51 is amplifiedby an amplifier 52 and supplied to a frequency converter 53, in which itis frequency-converted into a baseband signal by use of a receptioncarrier supplied to a reception carrier input terminal 54. The basebandsignal thus frequency-converted by the frequency converter 53 issupplied to five carrier multipliers 55, 56, 57, 58, 59. Carrier signalshaving different frequencies supplied to first, second, third, fourthand fifth carrier input terminals 61, 62, 63, 64, 65 are supplied to thecarrier multipliers 55, 56, 57, 58, 59. Therefore, the carriermultipliers 55, 56, 57, 58, 59 multiply the baseband signals suppliedthereto with the corresponding carrier signals to provide demodulatedsignals.

The frequencies of the carrier signals supplied to the first, second,third, fourth and fifth carrier input terminals 61, 62, 63, 64, 65 areselected to be the same as those of the carrier signals supplied to theterminals 16, 17, 18, 19, 20 of the transmission circuit shown in FIG.1.

The demodulated signals from the carrier multipliers 55 through 59 aresupplied through switches 66, 67, 68, 69, 70 to integrators 72, 73, 74,75, 76, respectively. The switches 66, 67, 68, 69, 70 are turned on andoff based on a switching control signal supplied to a control signalinput terminal 71. The switches 66, 67, 68, 69, 70 are simultaneouslyturned on and off under the control of the switching control signalsupplied thereto through the control signal input terminal 71.

Each of the switches 66 through 70 is turned on and off at every onemodulation unit of the transmitted signal. Specifically, although thetransmission side shown in FIG. 1 employs the time which results fromadding αT to the time during which the angular frequency ωs serving asthe frequency difference between the carriers is advanced by 2π everymodulation unit as one modulation unit, each of the switches 66 to 70 isclosed during the period T located at the central portion of onemodulation unit as shown in FIG. 7.

Therefore, when the switches 66 to 70 are closed during the centralperiod T of each modulation unit, the demodulated signals supplied fromthe carrier modulators 55 to 59 are integrated by the integrators 72 to76. In this embodiment, the thus integrated signals become phase dataindicative of amounts wherein phases are changed during the integratedperiod (i.e., one modulation unit period). Phase data detected by theintegrators 72 to 76 are represented as φ₀′, φ₁′, φ₂′, φ₃′, φ₄′,respectively.

A phase multiplier 77 multiplies the phase data φ₀′ detected by theintegrator 77 and the phase data φ₁′ detected by the integrator 73 todetect phase data Δφ₀′ based on a phase difference between the two phasedata φ₀′ and φ₁′. A phase multiplier 78 multiplies the phase data φ₁′detected by the integrator 73 and the phase data φ₂′ detected by theintegrator 74 to detect phase data Δφ₁′ based on a phase differencebetween the two phase data φ₁′ and φ₂′. A phase multiplier 79 multipliesthe phase data φ₂′ detected by the integrator 74 and the phase data φ₃′detected by the integrator 75 to detect phase data Δφ₂′ based on a phasedifference between the two phase data φ₂′ and φ₃′. Further, a phasemultiplier 80 multiplies the phase data φ₃′ detected by the integrator75 and the phase data φ₄′ detected by the integrator 76 to detect phasedata Δφ₄′ based on a phase difference between the two phase data φ₃′ andφ₄′.

The phase data Δφ₀′, Δφ₁′, Δφ₂′, Δφ₃′ detected by the phase multipliers77, 78, 79, 80 are supplied to phase data/reception data converters 81,82, 83, 84, respectively. The phase data/reception data converters 81 to84 carry out conversions reverse to those that had been carried out bythe transmission data/phase data converters 2, 3, 4, 5 when thetransmission signal is transmitted. Specifically, the phasedata/reception data converters 81, 82, 83, 84 determine that the phasedata supplied thereto are closest to any one of the four phases (π/4,3π/4, −3π/4, −π/4) shown in the aforesaid table 1, and then convert thusdetermined phase values into 2-bit [X, Y] data shown in the table 1.

Some suitable means (not shown) synthesizes 2-bit data thus obtainedfrom the converters 81 to 84 to provide 8-bit data and the 8-bit data isoutput from a reception data output terminal 85.

When the above-mentioned transmission processing and the above-mentionedreception processing are carried out, the bit data obtained at theterminal 1 of the transmission side is transmitted via radio waves andobtained at the terminal 85 of the reception side. Although atransmission processing in this case is a so-called multi-carrier systemwherein a signal is transmitted by use of a plurality of carriers, it isa processing wherein data is transmitted based on the phase differencebetween the carriers. Accordingly, the reception side detectstransmission data only by detecting the phase difference after the phaseof each carrier had been detected. Therefore, unlike the case that datais modulated in the carrier, a transmission clock need not bereproduced. Hence, data can be transmitted and received by a simplecircuit arrangement which does not need a complicated synchronizingcircuit such as a PLL (phase-locked loop) circuit.

According to the inventive transmission processing, since only phasedifference information is transmitted, data can be transmitted withsmall intersymbol interference even in a transmission line having alarge dispersion of delay. Therefore, even when the communication systemaccording to the present invention is applied to a transmission systemsuch as a mobile communication system, for example, data can betransmitted accurately. In this case, a dynamic range of a communicationwaveform can be minimized without a deterioration of transmissioncharacteristic and an interference to the adjacent channel can beminimized. Further, an interference from the adjacent channel can beavoided even if a timing shift is allowed a little. Moreover, it ispossible to remove the influence exerted by each carrier provided forthe respective channels upon the other carriers.

Further, since the carrier need not be reproduced by a PLL circuit onthe reception side, even when the reception condition is notsatisfactory and a signal-to-noise ratio (S/N) is low, it becomespossible to receive data satisfactorily.

Furthermore, according to this embodiment, since one modulation unit onthe transmission side is given the small additional time period (αT inthe equation (1)) and the phase is detected during the period from whichthe addition time period is removed on the reception side, it becomespossible to satisfactorily receive data from this standpoint.

Furthermore, according to this embodiment, since the transmission systemis composed of the limiter 31 for amplitude-limiting the mixed signal ofthe modulated carriers and the filter 32 for filtering out the output ofthe limiter 31 to limit the amplitude about 1.5 times as high as thestandard deviation of the amplitude distribution, even though thepeak-to-peak value of the transmission waveform is increased when thecarriers are mixed, it is possible to transmit data satisfactorilywithout distorting the transmission waveform.

The processing system composed of the limiter 31 and the filter 32 canbe applied to a transmission circuit of other systems than thetransmission circuit according to this embodiment, i.e., variouscircuits which can output modulated output waveforms wherein aprobability distribution of amplitude is approximate to a Gaussiandistribution.

While the amplitude about 1.5 times the standard deviation of theamplitude distribution is limited as described above, the presentinvention is not limited thereto and an amplitude is limited by apredetermined value of more than 1.5 times of the standard deviation ofthe amplitude distribution.

Further, while the 2-bit of 8-bit data are converted into the phasedifference data and transmitted by use of five carriers as describedabove, the present invention is not limited thereto and much more datacan simultaneously be transmitted by use of many more carriers or thenumber of carriers can be lessened.

As the transmission processing and the reception processing, there canbe used other transmission processing and reception processing so longas they can transmit data based on the phase difference between thecarriers.

The reason that data can be satisfactorily transmitted based on thephase difference between the carriers according to this embodiment willbe described with reference to the following equations. A waveform ofthe transmission signal obtained by the transmission circuit shown inFIG. 1 is expressed by the following equation (2): $\begin{matrix}{{x(t)} = {\sum\limits_{L = 0}^{N}{^{{- {j\varphi}}\quad L}^{{- {j{({{\omega \quad c} + {L\quad \omega \quad s}})}}}t}}}} & (2)\end{matrix}$

In the case of the arrangement shown in FIG. 1, since five carriers areused to transmit the phase difference, N in the equation (2) becomes 4.The equation (2) indicates that the four carriers are spaced apart infrequency by ωs. In the equation (2), ωc represents a transmissionfrequency (i.e., frequency converted by the frequency converter 33 inFIG. 3).

Then, if the transmission line has no delayed wave or the like, then aphase φ_(p) modulated by Pth carrier is obtained by the followingequation (3):

Te ^(∫φp′)=∫_((T)) X(t)e ^(+j(ωc+pωs)t) dt  (3)

(T) is the time of period which includes the modulated signal of onemodulation unit. Expanding the equation (3), we have: $\begin{matrix}\begin{matrix}{{T\quad ^{j\quad \varphi \quad p^{\prime}}} = \quad {\int_{(T)}{\sum\limits_{L = 0}^{N}{^{j\quad \varphi}L\quad ^{{- j}\quad {({p - L})}\omega}s^{t}{t}}}}} \\{= \quad {T\quad ^{j\quad \varphi \quad p}}}\end{matrix} & (4)\end{matrix}$

Accordingly, the above-mentioned equation (4) reveals that the phaseφ_(p) modulated on the transmission side and the phase φ_(p)′demodulated on the reception side are equal to each other so that aperfect transmission is possible. Assuming now that the transmissionline has a delay dispersion, then an impulse response thereof isexpressed by the following equation (5): $\begin{matrix}{{m(t)}\overset{\Delta}{=}{\sum\limits_{k = 0}^{M - 1}{m_{k}{\delta \left( {t - \tau_{k}} \right)}}}} & (5)\end{matrix}$

In the equation (5), M represents the number of delayed waves, τkrepresents the delay time of each delay path and mk represents a complexnumber amplitude of each delay path. If the impulse response is obtainedas described above, then the reception signal can be obtained bycomposing the equations (2) and (3) and therefore obtained by thefollowing equation (6): $\begin{matrix}\begin{matrix}{{\gamma (t)}\overset{\Delta}{=}\quad {{x(t)}*{m(t)}}} \\{= \quad {\sum\limits_{L = 0}^{N}{\sum\limits_{k = 0}^{M - 1}{{mk}\quad ^{j\quad {pL}}^{{- {j{({{\omega \quad c} + {L\quad \omega \quad s}})}}}{({t - {\tau \quad k}})}}}}}}\end{matrix} & (6)\end{matrix}$

Under the condition that the transmission path has the delay dispersion,the phase φ_(p)′ demodulated on the reception side is obtained by thefollowing equation: $\begin{matrix}\begin{matrix}{{T\quad ^{j\quad \varphi \quad p^{\prime}}} = \quad {\int_{(T)}{{\gamma (t)}^{{+ {j{({{\omega \quad c} + {p\quad \omega \quad s}})}}}t}\quad {t}}}} \\{= \quad {\int_{(T)}{\sum\limits_{L = 0}^{N}{\sum\limits_{k = 0}^{M - 1}{{mk}\quad ^{{({{\omega \quad c} + {L\quad \omega \quad s}})}k}\quad ^{j\quad \varphi \quad L}^{{j{({p - L})}}\omega \quad {st}}{t}}}}}} \\{= \quad {T\quad ^{{j\varphi}\quad p}{\sum\limits_{k = 0}^{M - 1}{{mk}\quad ^{{+ {j{({{\omega \quad c} + {p\quad \omega \quad s}})}}}\tau \quad k}}}}}\end{matrix} & (7)\end{matrix}$

Inasmuch as a differential phase Δφ_(p)′ detected on the reception sideis a difference between (P+1)th carrier phase and Pth carrier phase, itcan be obtained by the following equation (8): (8) $\begin{matrix}{^{j\quad {\Delta\varphi}\quad p^{\prime}} = {^{{j\quad \varphi \quad p} + 1^{\prime}}^{{- j}\quad \varphi \quad p^{\prime}}}} \\{= {^{{j\quad \varphi \quad p} + 1}^{{- j}\quad \varphi \quad p}{\sum\limits_{k = 0}^{M - 1}{{mk}\quad ^{{- {j{({{\omega \quad c} + {{({p - 1})}\omega \quad s}})}}}\tau \quad k}{\sum\limits_{l = 0}^{M - 1}{\overset{*}{m}\quad 1^{{- {j{({{\omega \quad c} + {p\quad \omega \quad s}})}}}\tau}}}}}}} \\{= {^{j\quad {\Delta\varphi}\quad p}\left\lbrack {^{j\quad \omega \quad s\quad \tau \quad k} \times \left\{ {{{mk}}^{2} + {\sum\limits_{L > k}^{M - 1}{2\quad {Re}\left\{ {m\quad k\quad \overset{*}{m}\quad e} \right\} \cos \left\{ {\left( {{\omega \quad c} + {p\quad \omega \quad s}} \right)\left( {{\tau \quad k} - {\tau \quad l}} \right)} \right\}}}} \right\}} \right\rbrack}}\end{matrix}$

If now the modulation time T is selected to be sufficiently larger thanthe delay dispersion τk, then we have the following equations (9) and(10):

 τk<T  (9)

e ^(jωsτk)=1  (10)

Therefore, phase information φ_(p)′ demodulated on the reception side isprovided by multiplying phase information φ_(p) transmitted from thetransmission side with real number term a_(p) and expressed by thefollowing equation (11):

e ^(jΔφp′) =e ^(jΔφp) a _(p)  (11)

The above-mentioned equation (11) reveals that the real number does notaffect phase information so that phase information can be transmittedaccurately. Also, there occurs no intersymbol interference.

The description that had been made so far by use of the equations can beapplied to other modulated waves allocated on the adjacent channels. Itis clear that other channels can be prevented from being affected by asmall timing shift.

Having examined by use of the above-mentioned equations that thecommunication system according to the present invention is applied tothe mobile communication system in actual practice, in a cellular systemwherein a telecommunication is made between a base station and aterminal station serving as a mobile station in the service area over aradius of 1 km from the base station, for example, a delay dispersionfalls in a range of about 10 to 20 microseconds. Moreover, it is assumedthat a time fluctuation period due to the fading falls in a range ofabout {fraction (1/100)} Hz=10000 microseconds where a carrier frequencyis 800 MHz and a moving speed of the terminal station is 100km/hour. Ifthe communication system according to this embodiment is used under theabove-mentioned conditions, the modulation time T of one modulation unitfalls in a range of about 100 to 1000 microseconds.

A communication system according to a second embodiment of the presentinvention will be described with reference to FIGS. 8 and 9. In FIGS. 8and 9, like parts corresponding to those of FIGS. 1 to 7 are marked withthe same references and therefore need not be described in detail.

According to this embodiment, similar to the example shown in FIG. 1,the present invention is applied to a communication system whereindigital data is transmitted and received via radio waves. FIG. 8 showsan arrangement of a transmission system. The transmission processingcircuit shown in FIG. 8 is the same in arrangement as that of thetransmission processing circuit shown in FIG. 1 where the outputs of thecarrier multipliers 11 to 15 are mixed by the mixer 21. Then, the outputof the mixer 21 is supplied to a multiplier 24 for multiplying a timewaveform. A time waveform output from a time waveform generator 23 ismultiplied with a transmission signal at every modulation unit by themultiplier 23 and a multiplied signal is supplied to an output terminal22.

FIG. 9 shows an example of a time waveform output from the time waveformgenerator 23. This time waveform is multiplied with the transmissionsignal at every modulation unit. A data format of one modulation unitwill be described initially. One modulation unit Tm is the time havingthe spare time αT shown in the equation (1). This spare time αT isdivided into two portions (α/2)T and located before and after thecentral data body portion T.

This time waveform holds a constant level at the central data bodyportion T. Of the spare times (α/2)T located before and after the databody portion T, predetermined intervals (interval from −T_(G) to 0 andinterval from T to T+T_(G)) adjoining the data body portion T areemployed as guard time portions. The guard time portions have thewaveform having the same constant level as that of the data body portionT. Remaining spare time portions are employed as lamp portions (intervalfrom −T_(G)−T_(R) to T_(G) and interval from T+T_(G)+T_(R)). These rampportions have waveforms which are raised to the constant level. Theraised waveform is the waveform of a curve shown by odd function(odd-symmetry function in the leading and trailing edges) of a linearsine (or cosine) function.

The above-mentioned time waveform is multiplied with the transmissionsignal, whereby the reception side for receiving the transmission signalcan receive a signal of every modulation unit with ease. In particular,the time waveform is selected to be the time waveform which changes inthe form of a curve such as a sine wave in the ramp portions. Therefore,since the time waveform is multiplied with the transmission signal, ahigher harmonic is not generated and digital data can be transmittedsatisfactorily.

A communication system according to a third embodiment of the presentinvention will be described with reference to FIG. 10. In FIG. 10, likeparts corresponding to those of FIGS. 1 to 9 are marked with the samereferences and therefore need not be described in detail.

According to this embodiment, similar to the example shown in FIG. 1,the present invention is applied to a communication system whereindigital data is transmitted and received via radio waves. Thetransmission processing circuit shown in FIG. 10 is arranged as acircuit for multiplying a transmission signal with a time waveformsimilar to the transmission processing circuit shown in FIG. 8. In thisembodiment, carrier signals having different frequencies obtained at thefirst, second, third, fourth and fifth carrier input terminals 16, 17,18, 19 and 20 are supplied to multipliers 16 a, 17 a, 18 a, 19 a and 20a, in which they are multiplied with time waveforms of every modulationunit output from the time waveform generator 23. The carrier signalshaving different frequencies multiplied with time waveforms are suppliedto the carrier multipliers 11, 12, 13, 14 and 15, in which they aremultiplied with the phase data φ₀, φ₁, φ₂, φ₃, φ₄.

The time waveform of every modulation unit output from the time waveformgenerator 23 becomes such as the one shown in FIG. 9.

A rest of the arrangement is similar to that of the transmissionprocessing circuit shown in the example of FIG. 8.

Since the carrier signals are directly multiplied with the timewaveforms, a transmission signal similar to that obtained when the timewaveform is multiplied with the signal which results from mixing thesignals modulated by the carrier signals. Therefore, it becomes possiblefor the reception side to receive the transmission signal of onemodulated unit with ease.

A communication system according to a fourth embodiment of the presentinvention will be described with reference to FIG. 11. In FIG. 11, likeparts corresponding to those of FIGS. 1 to 10 are marked with the samereferences and therefore need not be described in detail.

In this embodiment, multiplied signals are directly output instead ofmultiplying the carriers with the time waveforms shown in FIG. 10.Specifically, as shown in FIG. 11, there are provided carrier/timemultiplied waveform generators 24 a, 24 b, 24 c, 24 d, 24 e. Thegenerators 24 a, 24 b, 24 c, 24 d, 24 e generate multiplied signalswhere first, second, third, fourth and fifth carriers are multipliedwith the time waveform shown in FIG. 9. Outputs of the generators 24 ato 24 e are supplied to the carrier multipliers 11, 12, 13, 14, 15,respectively.

The rest of the arrangement is similar to that of the transmissionprocessing circuit shown in FIG. 10.

In accordance with this embodiment, it is possible to obtain themultiplied signals wherein the carriers are multiplied with timewaveforms by a simple arrangement which does not need the multipliers.Specifically, since the curve portion of the time waveform is a sinewave, a multiplication of the sine wave function can be converted into asum of two trigonometric functions and a division of 2^(n) on the basisof an addition theorem of trigonometric function. Therefore, thecarrier/time multiplied waveform generators 24 a to 24 e can be realizedby simple circuit arrangements which do not need multiplication.

The fact that the multiplied signals of the time waveform and thecarriers can be realized by the simple circuit arrangements which do notneed multiplication will be described with reference to the followingequations. A signal obtained at the output terminal 22 when the timewaveform is multiplied with the carriers is expressed by the followingequation (12): $\begin{matrix}{{{x(t)} = {{u(t)}{\sum\limits_{L = 0}^{4}{^{j\quad \varphi \quad L} \times ^{j\quad L\quad \omega \quad {ct}}}}}}{{u(t)} = \quad \quad \left\lbrack \begin{matrix}\begin{matrix}\begin{matrix}{1:{{- T_{G}} \leq t < {T + T_{G}}}} \\{0:{t < {{- T_{R}} - {T_{G}t}} \geq {T + T_{G} + T_{G}}}}\end{matrix} \\{{\frac{1}{2}\left\lbrack {1 - {\cos \left\{ {\frac{\pi}{T_{R}}\left( {t + T_{G} + {\frac{1}{2}T_{R}}} \right)} \right\}}} \right\rbrack}:{{{- T_{R}} - T_{G}} \leq t < {- T_{G}}}}\end{matrix} \\{{\frac{1}{2}\left\lbrack {1 + {\cos \left\{ {\frac{\pi}{T_{R}}\left( {t - T_{G} - {\frac{1}{2}T_{R}}} \right)} \right\}}} \right\rbrack}:{{T + T_{G}} \leq t < {T + T_{R} + T_{G}}}}\end{matrix} \right.}} & (12)\end{matrix}$

where ω_(c)=2π/T.

Then, the output signals of the carrier/time multiplied waveformgenerators 24 a to 24 e are presented as follows in response to 1=0, 1 .. . 4.

y _(L)(t)=u(t)e ^(jLωct)  (13)

A calculation of Y_(L)(t) is effected by a simple equation withoutquadratic expression of trigonometric functions and expressed by thefollowing equation (14) during the interval of −T_(R)−T_(c)≦t<−T_(G).$\begin{matrix}{{y_{L}(t)} = {{\frac{1}{2}\left\lbrack {1 - {\cos \left\{ {\frac{\pi}{T_{R}}\left( {t + T_{G} + {\frac{1}{2}T_{R}}} \right)} \right\}}} \right\rbrack}\left\{ {{\cos \left( {1\omega \quad {ct}} \right)} + {j\quad {\sin \left( {1\quad \omega \quad {ct}} \right)}}} \right\}}} & (14)\end{matrix}$

If the equation (14) is substituted with α and β as follows:$\begin{matrix}{{\alpha = {\frac{\pi}{T_{R}}\left( {t + T_{G} + {\frac{1}{2}T_{R}}} \right)}}{\beta = {1\omega_{c}t}}} & (15)\end{matrix}$

 β=1ω_(c) t  (15)

If the equations (14) is replaced with the equation (15) as describedabove, it is possible to obtain the multiplied signal of the carrier andthe time waveform expressed by the following equation (16):$\begin{matrix}\begin{matrix}{{Y_{L}(t)} = \quad {\frac{1}{2}\left\{ {1 - {\cos \quad \alpha}} \right\} \left\{ {{\cos \quad \beta} + {j\quad \sin \quad \beta}} \right\}}} \\{= \quad {{\frac{1}{2}\left\{ {{\cos \quad \beta} - {\cos \left( {\alpha + \beta} \right)} - {\cos \left( {\alpha - \beta} \right)}} \right\}} -}} \\{\quad {\frac{1}{2}j\left\{ {{\sin \quad \beta} - {\sin \left( {\alpha + \beta} \right)} - {\sin \left( {\alpha - \beta} \right)}} \right\}}}\end{matrix} & (16)\end{matrix}$

Further, the multiplied signals of the carriers and the time waveformcan be obtained by the similar calculation during the interval ofT+T_(G)≦t<T+T_(G)+T_(R). Accordingly, the output signals from thecarrier/time multiplied waveform generators 24 a to 24 e can be obtainedby the calculation of the sum of trigonometric functions and the simpledivision.

In actual practice, each of the carrier/time multiplied waveformgenerators 24 a to 24 e may include a ROM table (memory) in which thereare stored values of respective sample points of time waveforms and aROM table in which that are stored values of respective sample points ofcarriers having different frequencies. Then, the multiplied signals canbe obtained by calculating the values read out from the two ROM tablesin accordance with the above-mentioned equations. Alternatively, thereis provided a ROM table in which there are stored values which resultfrom analyzing multiplied values of the carriers and the time waveformsobtained at respective sample points obtained by the above-mentionedcalculation. Then, the above-mentioned values may be sequentially readout from the ROM table.

The simplified arrangement for multiplying the carriers having differentfrequencies and the time waveforms can be applied to other communicationsystem than the communication system in which data can be transmittedbased on the phase difference between the carriers. Specifically, thepresent invention can be applied to any one of a multi-carrier systemfor transmitting a plurality of carriers and a system using a singlecarrier so long as the system is a transmission system in which timewaveforms have to be superimposed continuously. The circuit arrangementnecessary for a calculation processing can be simplified.

A communication system according to a fifth embodiment of the presentinvention will be described with reference to FIGS. 12 and 13. In FIGS.12 and 13, like parts corresponding to those of FIGS. 1 to 11 are markedwith the same references and therefore need not be described in detail.

In this embodiment, the present invention is applied to the transmissionprocessing circuit of the communication system wherein digital data istransmitted and received similarly to the example shown in FIG. 1.According to this embodiment, the processing for multiplying carriersand phase data can be simplified. Specifically, the transmissionprocessing circuit is arranged as shown in FIG. 12. As shown in FIG. 12,the initial phase data φ₀ output from the reference phase data generator6 shown in FIG. 1 is supplied to a ω₀ waveform generator 25 a, the phasedata φ₁ output from the phase multiplier 7 is supplied to a ω₁ waveformgenerator 25 b, the phase data φ₂ output from the phase multiplier 8 issupplied to a ω₂ waveform generator 25 c, the phase data φ₃ output fromthe phase multiplier 9 is supplied to a ω₃ waveform generator 25 d, andthe phase data φ₄ output from the phase multiplier 10 is supplied to aω₄ waveform generator 25 e, respectively. The above-mentioned generators25 a to 25 e take the phase data supplied thereto at every onemodulation unit as the initial phase values and add phase values to theinitial phase values at every sample interval sequentially to therebyobtain carrier-modulated phase data. Thus, there can be obtainedphase-modulated transmission signals. A mixer 21 mixes the transmissionsignals supplied thereto to provide a mixed signal of supplied to thetransmission signal output terminal 22.

The rest of the arrangement is similar to that of the transmissioncircuit shown in FIG. 1.

FIG. 13 shows an arrangement of each of the ω_(n) waveform generators 25a to 25 e. As shown in FIG. 13, phase data supplied to an input terminal101 is supplied to a complex phase/phase angle converter 102, in whichphase data is judged and converted into angle data. If phase data isfour-phase modulated data, then it is sufficient to determine in whichquadrant the phase data exists. Therefore, it is sufficient that thefour angle data are provided as conversion values.

Resultant angle data is supplied through a switch 103 to a phaseangle/complex phase converter 107 as an initial phase value and is alsosupplied through a delay circuit 104 to an adder 105. The phaseangle/complex phase converter 107 converts data read out from thetrigonometric function ROM table 108 into a complex phase waveformsignal. The complex phase waveform signal thus converted is output froman output terminal 109.

The initial phase value supplied through the delay circuit 104 to theadder 105 is added with an output of n-times data generator 106 forgenerating n-times data of the phase angle of one sample. An output ofthe adder 105 is supplied through the switch 103 to the phaseangle/complex phase converter 107 and from the delay circuit 104 to theadder 105.

Accordingly, in the initial state, the switch 103 is connected to thecomplex phase/phase angle converter 102 side and then changed inposition to the adder 105 side, whereby n-times data of the phase angleof one sample is sequentially added at every sample and then supplied tothe phase angle/complex phase converter 107. Thus, the complex phasewaveform output from the output terminal 109 becomes a signal whichresults from directly modulating (complex) phase data by the carrier.

Since the signal, which is directly modulated by the carrier, isobtained, the carrier multipliers 11 to 15 shown in FIG. 1 need not beprovided, thereby making it possible to reduce the circuit scale of themulti-carrier system transmission circuit and to lessen an amount ofcalculation processing.

While the present invention is applied to the communication systemwherein data is transmitted based on the phase difference between thecarriers as described above, the present invention is not limitedthereto and can be applied to other communication systems so long asthey are of the multi-carrier system for simultaneously transmitting aplurality of carriers.

A communication system according to a sixth embodiment of the presentinvention will be described with reference to FIGS. 14 and 15. In FIGS.14 and 15, like parts corresponding to those of FIGS. 1 to 13 are markedwith the same references and therefore need not be described in detail.

In this embodiment, the present invention is applied to a receptionprocessing circuit of the communication system in which digital data istransmitted and received via radio waves similarly to the example shownin FIG. 6 and in which a reception signal is multiplied with the timewaveform. FIG. 14 shows a reception processing circuit wherein thesignal demodulated to the baseband signal by the mixer 53 shown in FIG.6 is processed. In this embodiment, the baseband signal is a signalwhich results from orthogonally modulating signals of I component and Qcomponent. The I component signal is supplied from a terminal 86 a to aone-bit system analog-to-digital (A/D) converter 87 a. The Q componentsignal is supplied from a terminal 86 b to a one-bit system A/Dconverter 87 b.

Each of the one-bit system A/D converters 87 a, 87 b outputs data of 1or −1 as one-bit output. Therefore, when outputs of the two A/Dconverters 87 a, 87 b are combined, there can be obtained two-bitoutputs of [1, 1], [1, −1], [−1, 1] and [−1, −1]. Incidentally, each ofthe A/D converters 87 a, 87 b is a converter capable of sampling data at2^(n) times (e.g., 64 times). Outputs from the A/D converters 87 a, 87 bare supplied to five carrier multipliers 55, 56, 57, 58, 59.

Then, carriers having different frequencies obtained at input terminals61, 62, 63, 64, 65 are supplied to multipliers 61 a, 62 a, 63 a, 64 a,65 a, respectively. Each of the multipliers 61 a through 65 a multipliesthe carrier with a time waveform output from a time waveform generator91. The time waveform generator 91 generates a time waveform of anarrangement shown in FIG. 15 at every one modulation unit.

Specifically, as shown in FIG. 15, this time waveform is composed of adata body portion interval T and ramp time portions of predeterminedperiod βT formed at a starting portion (timing of time zero) and anending portion (timing of time T) of the data body portion interval T.In this case, the center of the ramp portion becomes a boundary portionof the data body portion and the ramp portions are extended from theboundary portions 0 and T by (β/2)T. Waveforms of the front and rearramp time portions are curves of a linear function such as a sine waveand an odd function (function which becomes odd symmetry). In thisembodiment, the (β/2)T intervals, which are the extended intervals ofthe ramp time portions are made substantially coincident with theintervals (i.e., −T_(G) to 0 and T to T+T_(G)) of the guard timeportions of the modulation time waveform (see FIG. 9).

This demodulation time waveform is multiplied with complex conjugatevalues of respective carriers by the multipliers 61 a to 65 a. Asampling in this case is carried out at the same sampling rates of theA/D converters 87 a, 87 b.

Complex conjugate values in which the carriers are multiplied with thetime waveform are supplied to the carrier multipliers 55, 56, 57, 58,59, in which they are complex conjugate-multiplied with 2-bit outputs ofthe two A/D converters 87 a, 87 b. However, since the outputs of the A/Dconverters 87 a, 87 b are [1, 1], [1, −1], [−1 , 1] and [−1, −1], thecomplex conjugate-multiplication can be carried out by the addingprocessing.

Multiplied outputs of the carrier multipliers 55, 56, 57, 58, 59 aresupplied to integrators 72 a, 73 a, 74 a, 75 a, 76 a, respectively. Theintegrators 72 a, 73 a, 74 a, 75 a, 76 a are adapted to integrate dataat every one modulation unit during the period in which the timewaveform is multiplied and outputs phase data indicative of the amountin which the phase is changed during the integrating period.

The phase data output from the integrators 72 a, 73 a, 74 a, 75 a, 76 aare supplied to a differential demodulator 90, in which 2-bit data isdemodulated from each phase data. As a consequence, 8-bit demodulateddata in total is output to an output terminal 85. The differentialdemodulator 90 carries out the same demodulation processing as those ofthe phase multipliers 77 to 80 and the converters 81 to 84 according tothe first embodiment shown in FIG. 6.

A rest of the arrangement is similar to that of the reception circuitshown in FIG. 6.

When the reception processing is carried out as described above, thereception signal is multiplied with the time waveform at everymodulation unit and data transmitted at every one modulation unit can bedemodulated satisfactorily. In particular, since the sampling is carriedout by use of the one-bit system A/D converters, the carriers and thetime waveform can be multiplied by the simple circuit arrangement and bythe simple calculation. Therefore, as compared with the case that an A/Dconverter for producing data series of multi-value bits is used, it ispossible to simplify the circuit arrangement which is required to obtainthe same accuracy. Further, the processing circuit for multiplying thetime waveform of the shape shown in FIG. 15 functions as a low-passfilter for reducing a noise of a high frequency component of a receptionsignal. Therefore, the low-pass filter need not be combined into thecircuit and a satisfactory noiseless processing can be carried outwithout the low-pass filter.

A communication system according to a seventh embodiment of the presentinvention will be described with reference to FIG. 16. In FIG. 16, likeparts corresponding to those of FIGS. 1 to 15 are marked with the samereferences and therefore need not be described in detail.

In this embodiment, the multiplication processing of the time waveformand the carriers in the reception processing according to the sixthembodiment shown in FIG. 14 is simplified and the processing circuit isarranged as shown in FIG. 16.

Specifically, according to this embodiment, as shown in FIG. 16, thereare provided multiplied waveform generators 91 a, 91 b, 91 c, 91 d, 91 eat every carrier in order to directly obtain the multiplied signals ofthe time waveform and the carriers. Outputs of the multiplied waveformgenerators 91 a, 91 b, 91 c, 91 d, 91 e are supplied to the carriermultipliers 55, 56, 57, 58, 59, in which they are complexconjugate-multiplied with the reception signal.

The rest of the arrangement is similar to that of the reception circuitshown in FIG. 14.

In this embodiment, it is possible to obtain the multiplied signals ofthe carriers and the time waveform by the simple circuit arrangementcomposed of addition and bit-shifting.

The fact that the multiplied signals of the time waveform and thecarriers can be obtained by the simple circuit arrangement withoutmultiplication will be described with reference to the followingequations. A received baseband signal is expressed by the followingequation (17): $\begin{matrix}{{x(t)} = {{\sum\limits_{L = 0}^{4}{^{j\quad \varphi \quad L}^{{- j}\quad L\quad \omega \quad {st}}\frac{- 1}{2}T}} \leq t < {\left( {1 + \frac{a}{2}} \right)T}}} & (17)\end{matrix}$

In the above equation (17), φ_(L) is the phase of a signal which resultsfrom modulating information in a differential QPSK (quadrature phaseshift keying) fashion and ω_(s) is the fundamental carrier frequency. Inthis case, T=2π/ω_(s) is satisfied. Further, a is the ratio of the totallength of the ramp time portions and the guard time portions relative tothe data body portion. In this case, an inequality of a>0 is satisfied.

A sampling rate of the one-bit system A/D converter is selected to be Ntimes the fundamental carrier frequency ω_(s). N is the number of 2'spower and selected to be larger than the number (five) of carriers (N is64).

The time waveform has a shape defined by the following equation (18):$\begin{matrix}{{u(t)} = \left\lbrack \begin{matrix}{0,{t < {- \frac{\alpha \quad T}{2}}},{t \geq {T + \frac{\alpha \quad T}{2}}}} \\{1,{\frac{\alpha \quad T}{2} \leq T < {T - \frac{\alpha \quad T}{2}}}} \\{\frac{1}{2}\left\lbrack {\left. {1 + {\sin\left( {\frac{2\pi}{\alpha \quad T}t} \right.}} \right\rbrack,{{- \frac{\alpha \quad T}{2}} \leq t < \frac{\alpha \quad T}{2}}} \right.} \\{{\frac{1}{2}\left\lbrack {1 + {\sin \left\{ {\frac{2\pi}{\alpha \quad T}\left( {t - T} \right)} \right\}}} \right\rbrack},{{T - \frac{\alpha \quad T}{2}} \leq t < {T + \frac{\alpha \quad T}{2}}}}\end{matrix} \right.} & (18)\end{matrix}$

If α=⅛ and the time waveform is processed in a discrete fashion, then wehave: ${u(k)} = \left\lbrack {{\begin{matrix}{0,{k < {{- 4}\quad k} \geq 68}} \\{1,{4 \leq K < 60}} \\{{\frac{1}{2}\left\{ {1 + {\sin \left( {\frac{\pi}{4}k} \right)}} \right\}},{{- 4} \leq k < 4}} \\{{\frac{1}{2}\left\lbrack {1 - {\sin \left\{ {\frac{\pi}{4}\left( {k - 64} \right)} \right\}}} \right\rbrack},{60 \leq k < 68}}\end{matrix}{where}t} \equiv \frac{2\pi}{N\quad \omega \quad s}} \right.$

Then, the waveform of the carrier is processed at the sampling rate ofNω_(s) in a discrete fashion wherein ω_(L)=1ω_(s). The original waveformof the carrier is expressed by the following equation (20):$\begin{matrix}{{v_{L}(t)} = \left\lbrack \begin{matrix}{^{j\quad t\quad \omega \quad {st}},{{{- \frac{a}{2}}T} \leq t < \left( {1 + {\frac{a}{2}T}} \right)}} \\{0,{t < {- \frac{a\quad T}{2}}},{t \geq {\left( {1 + \frac{a}{2}} \right)T}}}\end{matrix} \right.} & (20)\end{matrix}$

If a is selected to be ¼ that is longer than the above-mentioned timewaveform and the carrier waveform is processed in a discrete fashion,then the original waveform of the carrier is expressed as:$\begin{matrix}{{v_{L}(m)} = \left\{ {{\begin{matrix}{{\quad {j2\pi}\quad \frac{L}{64}m},} & {{- 8} \leq m < 72} \\{0,{m < {- 8}},} & {m \geq 72}\end{matrix}{where}\quad t} \equiv {m\frac{2\pi}{N\quad \omega_{s}}}} \right.} & (21)\end{matrix}$

A multiplied value of the time waveform and the carriers is obtained asfollows: $\begin{matrix}{{{u(k)} \times {v_{L}(k)}} = \left\lbrack \begin{matrix}{0,{k < {{- 4}\quad k} \geq 68}} \\{^{j\quad 2\pi \quad \frac{L}{64}},{4 \leq k < 60}} \\{\frac{1}{2}\left\{ {1 + {\sin \left( {\frac{\pi}{4}k} \right)}} \right\} ^{{{j2}\quad \pi \quad \frac{L}{64}},{{- 4} \leq k < 4}}} \\{{{\frac{1}{2}\left\lbrack {1 - {\sin \left\{ {\frac{\pi}{4}\left( {k - 64} \right)} \right\}}} \right\rbrack}^{{j2\pi}\quad \frac{L}{64}k}},{60 \leq k < 68}}\end{matrix} \right.} & (22)\end{matrix}$

Sine and cosine tables are defined as follows. $\begin{matrix}{{{s(i)} = {{{\sin \left( {2\pi \quad \frac{i}{64}} \right)}0} \leq i < 64}}{{c(i)} = {{{\sin \left( {2\pi \quad \frac{i}{64}} \right)}0} \leq i < 64}}} & (23)\end{matrix}$

According to the sine and cosine tables, the multiplied value of thetime waveform and the carriers is expressed by the following equation(24): $\begin{matrix}{{{u(k)} \times {v_{L}(k)}} = \left\lbrack \begin{matrix}{0,{k < {- 4}}\quad,\quad {k \geq 68}} \\{{{c\left( {1k} \right)} + {{js}\left( {1k} \right)}},{4 \leq k < 60}} \\{{\frac{1}{2}\left\{ {1 + {s\left( {8k} \right)}} \right\} \times \left\{ {{c\left( {1k} \right)} + {{js}\left( {1k} \right)}} \right\}},{{- 4} < k < 4}} \\{{\frac{1}{2}\left\{ {1 - {s\left( {8k} \right)}} \right\} \times \left\{ {{c\left( {1k} \right)} + {{js}\left( {1k} \right)}} \right\}},{60 \leq k < 68}}\end{matrix} \right.} & (24)\end{matrix}$

Based on an addition theorem, the equation (24) can be substituted withthe following equation (25): $\begin{matrix}{{{S\left( {8k} \right)} \times \left\{ {{c\left( {1k} \right)} + {{js}\left( {1k} \right)}} \right\}} = {\frac{1}{2}\left\lbrack {\left\{ {{s\left( {{8k} + {1k}} \right)} + {s\left( {{8k} - {1k}} \right)}} \right\} + {j\left\{ {{c\left( {{8k} + {1k}} \right)} - {c\left( {{8k} - {1k}} \right)}} \right\}}} \right\rbrack}} & (25)\end{matrix}$

Study of the equation (25) reveals that u(k)×v1(k) can be realized bycalculation of index of tables, addition and division based onbit-shifting. Accordingly, the ROM tables and the simple calculationcircuit can constitute the generator which generates the multipliedsignals of the time waveform and the carriers.

A communication system according to an eighth embodiment of the presentinvention will hereinafter be described with reference to FIG. 17. InFIG. 17, like parts corresponding to those of FIGS. 1 to 16 are markedwith the same references and therefore need not be described in detail.

In this embodiment, there is provided a reception circuit for receivingand demodulating the transmission signal which had been modulated bymultiplication of the time waveform according to the second embodimentshown in FIG. 9. FIG. 17 shows a circuit arrangement for processing areceived baseband signal. As shown in FIG. 17, the received basebandsignal is supplied to an input terminal 111. This baseband signal issupplied to a time waveform multiplying circuit 112, wherein it ismultiplied with the time waveform shown in FIG. 9 at every onemodulation unit. The time waveform multiplying circuit 112 might beformed of a cosine rolloff filter. The resultant signal with which thetime waveform is multiplied is supplied to a sampling means (i.e., A/Dconverter) 113 where a sampling of 2×2^(N) is carried out. 2^(N) isselected to be larger than the number of carriers.

An output of the sampling means 113 is supplied to a fast Fouriertransform circuit (referred to hereinafter as “FFT circuit”) 114 whichoutputs demodulated signals of the number of the carriers by using dataat the sampling points obtained during a time twice as long as the databody portion (data obtained during the time 2T twice as long as the databody portion T as shown in FIG. 15) according to the calculation basedon the FFT. This demodulation processing is the same as that using thecarrier multipliers 55 to 59 shown in FIG. 6. The signal demodulatedfrom a plurality of carriers is supplied to a differential demodulator115 which demodulates data based on a phase difference of respectivesystems. The differential demodulator 115 is the demodulator whichcarries out the same demodulation as those carried out by the phasemultipliers 77 to 80 and the converters 81 to 84 in the first embodimentshown in FIG. 6. The demodulated data is obtained at an output terminal116.

According to the above-mentioned demodulation processing, since theboundary portions of the data body portion and the guard time portionsas the time waveform are odd-symmetrical waveforms, the time waveformserving as the gate signal does not contain the high frequency bandcomponent. Therefore, as compared with the case that the gate signal ofsquare wave is used, it is possible to lessen a noise obtained at otherfrequencies that a desired frequency.

A communication system according to a ninth embodiment of the presentinvention will be described with reference to FIGS. 18 to 21. In FIGS.18 to 21, like parts corresponding to those of FIGS. 1 to 17 are markedwith the same references and therefore need not be described in detail.

In this embodiment, there is provided a reception circuit for receivingand demodulating a transmission signal modulated by multiplication ofthe time waveform in the second embodiment shown in FIG. 9. Thisreception circuit can realize the demodulation processing shown in theeight embodiment of FIG. 17 by a simple circuit arrangement.Specifically, as shown in FIG. 18, the baseband signal applied to theinput terminal 111 is supplied to the time waveform multiplying circuit112, in which it is multiplied with the time waveform shown in FIG. 9 atevery one modulation unit. The signal multiplied with the time waveformis supplied to the sampling means (i.e., A/D converter) 113 whichcarries out a sampling of 2×2^(N) (2^(N) is the number of carriers orgreater).

An output of the sampling means 113 is supplied to a ramp portion addingcircuit 117. The ramp portion adding circuit 117 allow all data to beheld during the time T by adding data spaced apart from the center ofdata body portion by T/2 or greater to the points distant by T.Specifically, as shown in FIG. 19A, data at a ramp portion shown by alis added to a portion a2 which is distant from the ramp portion al by T.Also, data at a ramp portion shown by b1 is added to a portion b2 whichis distant from the portion b1 by T, thereby obtaining a waveformprovided when all data are gated by a certain square wave during thetime T, as shown in FIG. 19B. In the case of the modulated signal towhich the circuit according to this embodiment is applied, the signalbecomes the same signal at the position distant by the time T.Therefore, by the addition, phase information contained in the modulatedsignal can be prevented from being disturbed.

An output of the lamp portion adding circuit 117 is supplied to a FFTcircuit 118 which obtains demodulated signals of the number of carriersby use of data at the sampling points (2^(N) points) of time of the databody portion T according to the calculation of FFT. This demodulationprocessing is the same as that carried out by the carrier multipliers 55to 59 in FIG. 6. A signal demodulated from a plurality of carriers issupplied to the differential demodulator 115 which demodulates data onthe basis of phase difference of respective systems.

The rest of the arrangement is similar to that of the demodulationprocessing circuit shown in FIG. 17.

In the case of this embodiment, while the lamp portions are added anddata are demodulated by use of only data obtained at the sampling points(2^(N) points) during the time of the data body portion T at every onemodulation unit so that only the data obtained at the half samplingpoints as compared with the example shown in FIG. 17, it is possible toobtain exactly the same calculated results as those of the embodimentshown in FIG. 17. Accordingly, the amount of data is reduced to the halfand the amount of calculation processing can be lessened. As a result,the circuit arrangement can be simplified.

FIG. 20 shows the state that other frequencies than the desiredfrequency are attenuated when data is demodulated by the circuit shownin FIGS. 17 or 18. As compared with the case that the square wave isused as the time waveform (characteristic shown by solid curve in FIG.20), when the time waveform according to this embodiment is used(characteristic shown by dotted curve in FIG. 20), it is possible toconsiderably attenuate bands other than the band of the desiredfrequency.

The fact that the value obtained by processing the data by the FFTduring the time 2T (sampling points between −T and T with reference to 0as shown in FIG. 21) by the circuit shown in FIG. 17 and the valueobtained by processing data by the FFT during the time T (samplingpoints between −T/2 and T/2 with reference to 0 as shown in FIG. 21) bythe circuit shown in FIG. 18 will be described with reference to thefollowing equations.

If there exist d multi-carrier signals during the interval of −T/2≦t<T/2shown in FIG. 21 and a fundamental frequency of a carrier is ω_(c)=2π/T,then a signal x(t) is expressed as follows: $\begin{matrix}{{{x(t)} = {{u(t)}{\sum\limits_{L = 0}^{d - 1}{^{j\quad \varphi \quad L} \times ^{j\quad L\quad \omega \quad {ct}}}}}}{{u(t)} = \left\{ \begin{matrix}1 & {{t} \geq \frac{T}{2}} \\0 & {{t} > \frac{T}{2}}\end{matrix} \right.}} & (26)\end{matrix}$

where φ_(L) is phase information on the carrier.

If 2×2^(N) data are sampled during the 2T period, then the signal x(t)is expressed as follows: $\begin{matrix}{{{x_{n} \equiv {x\left( {\frac{T}{2^{N}}n} \right)}} = {u_{n}{\sum\limits_{L = 0}^{d - 1}{^{j\quad \varphi \quad L} \times ^{j\quad L\quad \omega \quad {ct}\quad \frac{T}{2^{N}}n}}}}}{u_{n} = \left\{ \begin{matrix}{1,{{- 2^{N - 1}} \leq n < 2^{N - 1}}} \\{0,,{n < {- 2^{N - 1}}},{n \geq 2^{N - 1}}}\end{matrix} \right.}} & (27)\end{matrix}$

The sampling frequency ω_(s) is expressed as ω_(s)=2^(N)×ω_(c). Sincethere are 2×2^(N) sampling points when the calculation of FFT iseffected during the interval of −T≦t<T, an output corresponding to thefollowing frequency can be obtained. $\begin{matrix}{{\omega_{k} = {{\frac{\omega_{s}}{2 \times 2^{N}} \times k} = {{\frac{k}{2}\omega_{c}k} = 0}}},1,{\ldots \quad 2^{N - 1}}} & (28)\end{matrix}$

Indexes of frequency that exist as a remarkable carrier are presented ask=2r and r=0, 1, . . . d−1. Therefore, the result obtained by thecalculation of the FFT is expressed by the following equation (29):$\begin{matrix}{{X_{k} \equiv {X\left( {\omega \quad}_{k} \right)}} = {\sum\limits_{n = {- 2^{N}}}^{2^{N - 1}}{\left\{ {u_{n}{\sum\limits_{L = 0}^{d - 1}{^{j\quad \varphi \quad L} \times ^{j\quad L\quad \omega \quad c\quad \frac{T}{2^{N}}}n}}} \right\} ^{{- j}\quad \omega \quad {k \cdot n \cdot T}}}}} & (29)\end{matrix}$

Then, if k is expressed by r and the characteristic of u_(n) is used,then the following equation is established: $\begin{matrix}{X_{r} = {\sum\limits_{n = {- 2^{M - 1}}}^{2^{N - 1} - 1}{\left\{ {\sum\limits_{L = 0}^{d - 1}{^{j\quad \varphi \quad L} \times ^{j\quad L\quad \omega \quad c\quad \frac{T}{2^{M}}}n}} \right\} ^{{- j}\quad r\quad \omega \quad {cn}\quad T}}}} & (30)\end{matrix}$

On the other hand, when the calculation of the FFT is carried out duringthe interval of −T/2≦t<T/2, there are 2^(N) sampling points so that anoutput corresponding to the following frequency can be obtained.$\begin{matrix}{{\omega_{k} = {{\frac{\omega_{s}}{2^{N}}k} = {{k\quad \omega_{c}\quad k} = 0}}},1,{\ldots \quad 2^{N - 1}}} & (31)\end{matrix}$

Indexes of frequency existing as a remarkable carrier are β=0, 1, . . .d−1. The result obtained by the calculation of the FFT is expressed bythe following equation (32) and a value of a frequency componentcorresponding to the remarkable index is expressed by the followingequation (33): $\begin{matrix}{{X_{k} \equiv {X\left( \omega_{k} \right)}} = {\sum\limits_{n = {- 2^{N - 1}}}^{2^{N - 1} - 1}{\left\{ {u_{n}{\sum\limits_{L = 0}^{d - 1}{^{j\quad \varphi \quad L} \times ^{j\quad L\quad \omega \quad c\quad \frac{T}{2^{N}}n}}}} \right\} ^{{- j}\quad \omega \quad {knT}}}}} & (32) \\{X_{\beta} = {\sum\limits_{n = {- 2^{N - 1}}}^{2^{N - 1} - 1}{\left\{ {\sum\limits_{l = 0}^{d - 1}{{^{j\quad \varphi \quad L} \cdot ^{j\quad L\quad \omega \quad c\quad \frac{T}{2^{N}}}}n}} \right\} ^{{- j}\quad {\varphi\omega}\quad {cnT}}}}} & (33)\end{matrix}$

The equation (33) is the same as the equation (30) and the calculationof the FFT for the time 2T and the calculation of the FFT for the time Toutput the same output for kωc (k=0, 1, . . . d−1).

Then, the reason that the calculated result of the FFT effected when theramp portions are added and the calculated result of the FFT effectedwhen the ramp portions are not added become the same for the necessaryfrequency (when a transmission line characteristic is flat) in thecircuit shown in FIG. 18 will be described below.

The time waveform shown in FIG. 22 is expressed by the followingequation (34): $\begin{matrix}\begin{matrix}{{x(t)} = {{v(t)}{\sum\limits_{L = 0}^{d - 1}{^{j\quad \varphi \quad L}^{j\quad L\quad \omega \quad {ct}}}}}} \\{{v(t)} = \left\lbrack \begin{matrix}{1:{{{- \frac{T}{2}}\left( {1 - \beta} \right)} \leq t < {\frac{T}{2}\left( {1 - \beta} \right)}}} \\{{0:{t < {{- \frac{T}{2}}\left( {1 + \beta} \right)}}},{t \geq {\frac{T}{2}\left( {1 + \beta} \right)}}} \\{{\frac{1}{2}\left\lbrack {1 + {\sin \left\{ {\frac{\pi}{\beta \quad T}\left( {t + \frac{T}{2}} \right)} \right\}}} \right\rbrack}:{{{- \frac{1}{2}}\left( {1 - \beta} \right)} \leq t < {{- \frac{T}{2}}\left( {1 - \beta} \right)}}} \\{{\frac{1}{2}\left\lbrack {1 - {\sin \left\{ {\frac{\pi}{\beta \quad T}\left( {t - \frac{T}{2}} \right)} \right\}}} \right\rbrack}:{{\frac{1}{2}\left( {1 - \beta} \right)} \leq t < {\frac{T}{2}\left( {1 + \beta} \right)}}}\end{matrix} \right.}\end{matrix} & (34)\end{matrix}$

If the calculated results of the Fourier transform of the continuoustime system are in agreement with each other, then it is to be notedthat the calculated results of the discrete FFT also are agreed witheach other. Therefore, the following equations (35) and (36) prove thatthe necessary frequencies are in agreement with each other.$\begin{matrix}{{X(\omega)} = {\int_{{- \frac{T}{2}}{({1 + \beta})}}^{\frac{T}{2}{({1 + \beta})}}{{v(t)}{\sum\limits_{L = 0}^{d - 1}{^{j\quad \varphi \quad L}{^{j\quad L\quad \omega \quad {ct}} \cdot ^{{- j}\quad \omega \quad t}}{t}}}}}} & (35) \\{{X^{\prime}(\omega)} = {\int_{- \frac{T}{2}}^{\frac{T}{2}}{\sum\limits_{L = 0}^{d - 1}{^{j\quad \varphi \quad L}^{j\quad L\quad \omega \quad {ct}} \times ^{{- j}\quad \omega \quad t}{t}}}}} & (36)\end{matrix}$

The equation (35) is modified as follows: $\begin{matrix}{{X(\omega)} = {{\int_{{- \frac{T}{2}}{({1 + \beta})}}^{\frac{T}{2}{({1 + \beta})}}{{\frac{1}{2}\left\lbrack {1 + {\sin \left\{ {\frac{\pi}{\beta \quad T}\left( {t + \frac{T}{2}} \right)} \right\}}} \right\rbrack}\quad {\sum\limits_{L = 0}^{d - 1}{^{j\quad \varphi \quad L}^{j\quad {({{t\quad \omega \quad c} - \omega})}t}{t}}}}} + {\int_{{- \frac{T}{2}}{({1 - \beta})}}^{\frac{T}{2}{({1 - \beta})}}\quad {\sum\limits_{L = 0}^{d - 1}{^{j\quad \varphi \quad L}^{j\quad {({{L\quad \omega \quad c} - \omega})}t}{t}}}} + {\int_{\frac{T}{2}{({1 - \beta})}}^{\frac{T}{2}{({1 + \beta})}}{{\frac{1}{2}\left\lbrack {1 - {\sin \left\{ {\frac{\pi}{B\quad T}\left( {t - \frac{T}{2}} \right)} \right\}}} \right\rbrack}\quad {\sum\limits_{L = 0}^{d - 1}{^{j\quad \varphi \quad L}^{j\quad {({{L\quad \omega \quad c} - \omega})}}{t}}}}}}} & (37)\end{matrix}$

Replacing the third term of the equation (37) with t′=t−T yields thefollowing equation (38):

The third term of the equation (37) is expressed as: $\begin{matrix}{= {\int_{{- \frac{T}{2}}{({1 + \beta})}}^{{- \frac{T}{2}}{({1 - \beta})}}{{\frac{1}{2}\left\lbrack {1 - {\sin \left\{ {\frac{\pi}{\beta \quad T}\left( {t^{\prime} + \frac{T}{2}} \right)} \right\}}} \right\rbrack}\quad {\sum\limits_{L = 0}^{d - 1}{^{j\quad \varphi \quad L} \times ^{{j\quad {({{L\quad \omega \quad c} - \omega})}t} - {\omega \quad T}}{t}}}}}} & (38)\end{matrix}$

If mω_(c) (m=0, 1, . . . d−1) is selected as ω, then the first terms ofthe equations (38) and (37) and other codes than the sine portions arein agreement with one another. Therefore, the equation (37) yields thefollowing equation (39) which can prove that the results of the additionof the ramp portion become the same. $\begin{matrix}{{X\left( {m\quad \omega \quad c} \right)} = {{{\int_{{- \frac{T}{2}}{({1 + \beta})}}^{{- \frac{T}{2}}{({1 - \beta})}}\quad {\sum\limits_{L = 0}^{d - 1}{^{j\quad \varphi \quad L}^{j\quad {({L - m})}\omega \quad {ct}}{t}}}} + {\int_{{- \frac{T}{2}}{({1 - \beta})}}^{\frac{T}{2}{({1 - \beta})}}\quad {\sum\limits_{L = 0}^{d - 1}{^{j\quad \varphi \quad L}^{j\quad {({L - m})}\omega \quad {ct}}{t}}}} + {\int_{- \frac{T}{2}}^{\frac{T}{2}}\quad {\sum\limits_{L = 0}^{d - 1}{^{j\quad \varphi \quad L}^{j\quad {({L - m})}\omega \quad {ct}}{{t\left( {\because\quad {{from}\quad {periodicity}}} \right)}}}}}} = {X^{\prime}\left( \quad {m\quad \omega_{c}} \right)}}} & (39)\end{matrix}$

According to the present invention, since a plurality of carriers havingdifferent frequencies are simultaneously transmitted and data aretransmitted on the basis of a phase difference between the carriers, itbecomes possible to demodulate transmitted data only by detecting thephase of each carrier.

In this case, since a plurality of carriers are converted into signalseach having a constant frequency interval, it becomes easy to detect thephase difference between the carriers.

The difference between the advanced phases of carriers during onemodulation unit time where the phase difference between the carriers tobe a multiple slightly larger than 2π and then transmitted. Thereception side detects transmitted data by judging the phase differenceof one modulation unit during a time where the difference between theadvanced phase of carriers becomes 2π. Thus, it is possible toaccurately detect transmitted data without being affected by intersymbolinterference or the like.

In each transmission processing, since the communication system includesthe limiter for amplitude-limiting a mixed signal of respectivemodulated carriers and the filter for filtering out the output of thelimiter wherein the limiter limits the amplitude at a rate about 1.5times or greater than the standard deviation of amplitude distributionand the output from the filter is transmitted, even though thepeak-to-peak value of the transmitted waveform becomes large when thecarriers are mixed, data can be satisfactorily transmitted without beingdeteriorated.

According to the present invention, since the communication systemincludes the modulating means for outputting a modulated output waveformin which the amplitude probability distribution is approximate to theGaussian distribution, the limiter for amplitude-limiting the outputwaveform of this modulating means and the filter for filtering out theoutput from this limiter wherein the limiter limits the amplitude at arate about 1.5 times or greater than the standard deviation of theamplitude distribution and the output of the filter is transmitted, thetransmission waveform having the large peak-to-peak value can besatisfactorily transmitted without being deteriorated.

Since the predetermined time waveform is multiplied with the carrier atevery one modulation unit time and then transmitted as theabove-mentioned transmission processing, it become easy for thereception side to detect the data transmitted based on the phasedifference.

When the time waveform is multiplied with the carriers, thepredetermined time waveform is multiplied with the carriers havingdifferent frequencies so that the multiplication of time waveforms canbe realized by the simple calculation.

When the predetermined time waveform is directly multiplied with thecarriers, there is provided the table for obtaining values which resultfrom analyzing the multiplied values of the carrier frequencies and thetime waveform so that the communication system can be realized by thesimple arrangement.

Since the phase values which are transmitted data are supplied asinitial phase values at every carrier and the phase values aresequentially added at every sample interval to thereby directly obtainthe phase-modulated signal, the phase-modulated signals can be directlyobtained by the simple arrangement using the ROM table without providingthe circuit for generating carriers.

Since a plurality of carriers having different frequencies aresimultaneously transmitted and the received signal is sampled by theone-bit system analog-to-digital converter and multiplied with the timewaveform, thereby demodulated as the reception processing means forreceiving data transmitted based on the phase difference between thecarriers, it is possible to obtain an accuracy equal to or higher thanthat obtained when the received signal is sampled by a multi-value-bitsystem analog-to-digital converter by the simple circuit arrangement.

When the received signal is sampled by the one-bit systemanalog-to-digital converter and demodulated, there are provided thegenerating means for generating signals which result from multiplyingthe carriers and the predetermined time waveform at every carrier andthe tables for obtaining the values which result from analyzing themultiplied values of the carrier frequencies and the time waveform areprovided as the respective generating means. Therefore, it is possibleto carry out the multiplication of the time waveform for demodulation bythe simple arrangement.

Upon reception processing, since the data body portion formed of onemodulation time is multiplied with the particular time waveform definedby the guard time portion accompanying with the data body portion andthe received signal is demodulated, it is possible to satisfactorilyextract the data body portion by the time waveform.

If the time waveform which is the odd symmetric waveform is provided atthe boundary between the data body portion and the guard time portionand which has the constant value in other portions, then it is possibleto satisfactorily demodulate data contained in the data body portionwithout noise.

Since the sampling means performs the sampling of the number of 2'spower which is larger than the number of carriers per modulation times,sample values of two modulation time are prepared about the data bodyportion of one modulation time and the sample values of two modulationtime are demodulated by a fast Fourier transform, it is possible torealize the demodulation processing by the simple circuit arrangement.

Furthermore, since the sampling means performs the sampling of thenumber of 2's power which is larger than the number of carriers permodulation time, sample values of the data body portion and the guardtime portion of one modulation time are prepared, the guard time portionof the sample values is added to the data body portion spaced by onemodulation time by the adding circuit and the sample value of onemodulation time obtained by the addition is demodulated by the fastFourier transform, it is possible to realize the demodulation processingby the simple circuit arrangement.

Having described preferred embodiments of the invention with referenceto the accompanying drawings, it is to be understood that the inventionis not limited to those precise embodiments and that various changes andmodifications could be effected therein by one skilled in the artwithout departing from the spirit or scope of the invention as definedin the appended claims.

What is claimed is:
 1. A communication system comprising: modulatingmeans for outputting a modulated output waveform in which an amplitudeprobability distribution is approximate to a Gaussian distribution; alimiter for amplitude-limiting said modulated output waveform of saidmodulating means; and a filter for filtering an output of said limiter,wherein said limiter amplitude-limits said modulated output waveform ata rate of about 1.5 times or greater of standard deviation of amplitudedistribution and an output of said filter is transmitted.
 2. Thecommunication system according to claim 1, wherein said modulating meanscomprises: converting means for converting transmission data into phasedifference data; means for generating reference phase data; multiplyingmeans for multiplying said reference phase data and said phasedifference data; first means for modulating said reference phase data bya carrier having a first frequency; second means for modulating phasedata output from said multiplying means by a plurality of carriershaving respective frequencies different from each other and from saidfirst frequency; and mixing means for mixing modulated signals outputfrom said first means for modulating and said second means formodulating to produce said modulated output waveform.
 3. Thecommunication system according to claim 2, wherein said modulating meanssets a difference between advanced phase of said plurality of carriersin one modulation unit time during which phase difference betweencarriers of said plurality of carriers is set to be a multiple slightlylarger than 2Π.
 4. The communication system according to claim 1,wherein said filter comprises a low-pass filter.